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Exponential Distribution

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Calculate the probability density function, lower cumulative probability, and upper cumulative probability of the exponential distribution.
Percentile x
x≧0
Scale parameter b
b＞0
\(\normalsize Exponential\ distribution\\ (1)\ probability\ density\\ \hspace{30px}f(x,b)={\large\frac{1}{b}e^{-\frac{x}{b}}}\\ (2)\ lower\ cumulative\ distribution\\ \hspace{30px}P(x,b)={\large\int_{\small 0}^{\small x}}f(t,b)dt={\large 1-e^{-\frac{x}{b}}}\\ (3)\ upper\ cumulative\ distribution\\ \hspace{30px}Q(x,b)={\large\int_{\small x}^{\small\infty}}f(t,b)dt={\large e^{-\frac{x}{b}}}\\\)

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